Convexity analysis in fixed income

Convexity is an issue that is confronted when planning hedged trades between eurodollar futures and futures contracts based on fixed-income securities, such as interest rate swaps and Treasury notes. A price curve for bonds, T-note futures and interest rate swap futures is convex in relationship with market yields. This means prices for these instruments rise more rapidly as yields fall than the price declines as yields rise — thus, a steeper curve when yields are low and a flatter curve for larger yields. Although the price curve of eurodollar futures is not convex, the convexity of other interest rate contracts indirectly determines eurodollar futures prices.

While the prices of fixed-interest securities change in varying amounts per basis point depending on current level of rates and yields, eurodollar futures prices change at $25 per basis point (1/4 year times $1,000,000 underlying notional principal times 0.01%). As yields fall, we expect the bond, T-note or swap price curve to increase up and away from eurodollar futures prices.

Conversely, when market yields increase, the eurodollar futures price will continue to drop at a constant dollar rate while the bond price drops at an increasingly slower rate, widening the distance between the two price curves.

Modified durations

“Convexity” (below) shows that as the market yield increases or decreases, deviations of the 10-year swap futures price from the eurodollar price straight line gradually expand. Although the differences appear small on the chart, the underlying security is a $100,000 interest rate swap in which dollar differences between the eurodollar and swap price curves are minor in relation to the swap futures price.